In general, spectra are recorded as values of amplitude, typically measured as a response to an excitation, as a function of wavelength (or the inverse of wavelength, namely frequency). In the field of spectral analysis, it is often necessary to calibrate or preprocess one or more spectra in order to be able to compare spectra or to extract information from spectra. One calibration or preprocessing approach is to normalize a spectrum or a set of spectra. Normalization may be required, for example, when comparing spectra having different amplitudes. In the case of optical spectra in particular, differences in amplitude may result from differences in a level of illumination, differences in a response of a detector, or differences in optical behavior of one sample as compared to another. Normalization is a process whereby the differences in instrument performance from spectrum to spectrum are reduced or eliminated.
Two common methods for normalizing spectral information are to normalize a spectrum to a maximum value of amplitude in the spectrum (“peak normalization”), and to normalize a spectrum to an area determined by integrating the spectrum over a range of wavelengths or frequencies (“area normalization”). Peak normalization is performed by dividing the amplitude at each point in a spectrum by the maximum amplitude of that individual spectrum. One obtains a normalized spectrum having intensities ranging from 1.0 at the location of the maximum to possibly as little as 0.0 where the spectral amplitude vanishes. Peak normalization in principle removes the variations in instrument behavior from spectrum to spectrum. However, peak normalization discards information about differences in samples that cause differences in amplitude of response to an invariant excitation. Such information can be very useful, but it is eliminated by normalizing all spectra in a set to a common maximum normalized amplitude of 1.0.
Peak normalization is based on a single amplitude value that appears in a spectrum. To the extent that this single value is incorrect, through a change in illumination intensity, instrumental misalignment, excessive noise in the data, or the like, the peak normalization method will give erroneous information.
Area normalization is another method of normalizing spectra in which the area under the spectrum is computed, for example by integrating the amplitude of the spectrum as a function of wavelength or frequency, and the entire spectrum is recomputed by dividing each value of amplitude by the value determined for the area. The resulting area normalized spectrum has an area of one area unit. However, the energy carried by electromagnetic radiation is proportional to the frequency, ν, of the radiation (e.g., Energy=hν), or equivalently, is inversely proportional to wavelength, λ, (i.e., Energy=hc/λ), where h is Planck's constant, and c is the speed of light. Therefore, an integration of amplitude over wavelength applies an equal “weight” to a unit of amplitude at long wavelength (i.e., low energy) as a unit of amplitude at short wavelength (i.e., high energy), even though one region may have a far different influence or effect than another, based on the energy content of the radiation.